第一HJ距离的理论分析

模型设定检验是资产定价的核心环节，作为模型误设的新指标，第一HJ距离受到学术界的广泛关注。然而，鲜有文献比较第一HJ距离和传统的误设测度的异同。本文系统地分析第一HJ距离的性质，并与传统的模型设定误差测度进行比较发现：（1）第一HJ距离将基于模型所用SDF的欧氏空间距离和最大定价误相联系，有丰富的经济含义；（2）第一HJ距离关注定价误差，相较于传统的模型误设测度，倾向于选择大的零Beta收益率和小的因子风险溢酬，对模型的排序有差异；（3）第一HJ距离的加权矩阵具有模型独立性和对测试资产组合选择的一致性。

Theoretical Analysis on the First HJ Distance

Model specification test is the key step of asset pricing, as a new model misspecification measure, the first HJ distance has been paid much academic attention. However, little studies concentrate on the similarities and differences between the first HJ distance and traditional measures. We analyzed the properties of the first HJ distance systematically, and compared with the traditional model specification measure in the paper, and found that: (1) the first HJ distance has linked the Euclidean space distance of the model SDF with the maximal pricing error, having ample economic meaning; (2) the first HJ distance focused on the pricing error, Compared with the traditional measures, the first HJ distance intended to choose the larger zero beta rate and smaller factor risk premium, and ranked the models differently; (3) the first HJ distance weighting matrix is model independent invariant to the test asset portfolio.